1. Field of the Invention
This invention relates to methods and apparatus for determining the intrinsic values of fracture toughness KIC and mixed mode fracture toughness for various structural materials such as steels, aluminum alloy, ceramics and metal-matrix composites using small spiral-grooved cylindrical specimens and pure torsional loading.
2. Background Information
The present invention determines fracture toughness KIC and mixed mode fracture toughness of solid materials utilizing a unique specimen design and loading condition in conjunction with a special finite element program. KIC is a material property that describes the material""s fracture resistance to brittle fracture initiation under full lateral constraint during static or xe2x80x9cquasistaticxe2x80x9d loading. The test methods that are currently used in many industries, including the nuclear industry, to evaluate fracture toughness may not fully conform to fracture mechanics theory. This is because the specimen size required to achieve complete control of the plane strain is prohibitively large. Hence, when critical flaw size and/or safe design stress is desired, KIC may be inferred from values derived from non-fracture-mechanics methods. Because the indirect methods inevitably contain large uncertainties, a large safety factor must be built into the design. With the invention, KIC is determined directly, without interpretation, allowing the uncertainty and safety factor associated with the safety assessment of fracture properties to be minimized.
In the present invention, a right cylindrical specimen having a spiral groove with a 45xc2x0 pitch is tested under pure torsion. A computer code, TOR3D-KIC, is then used to determine the mode I fracture toughness. Mixed mode fracture toughness values can be derived by varying the spiral pitch. TOR3D-KIC uses three-dimensional finite element techniques to analyze the crack tip opening displacement (CTOD) occurring on a non-coplanar 3-D spiral crack front. Special 3-D finite element meshes, with wedge singular elements at the crack front, were designed to simulate the 3-D spiral crack front and crack propagation orientation during transition phases of fatigue crack growth and the final fracture. Boundary conditions were assigned for the torsional loading configuration. Based on the input of the fracture load and final crack length, the CTOD at the crack flange along the crack front is analyzed and then integrated into the mode I fracture toughness formulation in conjunction with the minimum strain energy criteria.
The method can be used to determine the fracture toughness of graduated materials such as weldments and their heat-affected zones. Thus, the new method should be invaluable for the development of new structural materials and new welding technology, and it can be used in establishing new industry standards and regulatory guidelines.
The testing method that uses conventional compact tension specimens or their variations has a strong theoretical basis for use in determining fracture toughness, KIC. However, the downside of the method is the specimen size effect. Valid test result according to ASTM Test Method for Plane-Strain Fracture Toughness of Metallic Materials (E399), requires that both specimen thickness, B, and crack length, a, exceed 2.5(KIC/"sgr"YS)2, where "sgr"YS is the 0.2% offset yield strength of the material for temperature and loading rate of the test. If it is not possible to make a specimen from the available material that meets the criterion, then it is not possible to make a valid KIC measurement according to this method.
One prior method [Ref. 1] for KIC measurement under torsion uses a round specimen with a half penny-shaped crack making a 45xc2x0 angle with the specimen axis. This is basically a variation of tensile testing with a half penny shaped crack perpendicular to the tensile force. The latter type has been widely used in crack growth studies.
Our recent study [Ref. 2] demonstrated that the specimen size effects could be virtually eliminated using a cylindrical specimen subjected to pure torsion for KIC measurements.
[1] Sweeney, J., xe2x80x9cAnalysis of a Proposed Method for Toughness Measurements Using Torsion Testing,xe2x80x9d Journal of Strain Analysis, 1985, Vol. 20, No. 1, pp. 1-5.
[2.] Wang, J. A., Liu, K. C., McCabe, D. E., and David, S. A., xe2x80x9cUsing Torsional Bar Testing to Determine Fracture Toughness,xe2x80x9d Journal of Fatigue and Fracture for Engineering Materials and Structures, 2000, Vol. 23, pp. 917-927.
In a first embodiment of the invention, a method of determining fracture toughness KIC of a material comprises the steps of providing a cylindrical specimen having a helical groove at a 45xc2x0 pitch, applying pure torsion to the specimen, measuring the fracture torque, measuring the crack length, and calculating KIC from the fracture torque and the crack length.
The calculation of KIC is carried out with a computer program which comprises the steps of: establishing a finite element mesh for a cylindrical specimen under pure torsion to generate an equibiaxial tension/compression stress field on xc2x145xc2x0-pitched orthogonal planes of the finite elements along the right conoids, and a plane strain condition is maintained on every plane normal to the helical groove; establishing 3-D isoparametric finite element meshes with singular elements around the 3-D spiral crack front to simulate rxe2x88x92xc2xd singularity at the crack tip; simulating spiral crack front and crack propagation orientation along the right conoids; prescribing boundary conditions with free axial displacement to simulate pure torsion loading; applying initial end rotation to the finite element model with a given final crack length to determine the corresponding end torque; iterating the end torque step to match the end torque with the measured fracture torque to determine the final end rotation of the finite element model; determining the crack tip opening displacement based on the stress/strain field derived from the calculated final end rotation; verifying that the triaxial stresses and T-stress fields around the crack tip at fracture are positive to ensure a high constraint state is achieved; determining stress intensity factors KI, KII, and KIII from the crack tip opening displacement; and utilizing the stress intensity factors KI, KII, and KIII information and strain energy density criteria to determine the fracture toughness KIC.
In a second embodiment of the invention, a method of determining mixed mode fracture toughness of a material comprises the steps of providing a cylindrical specimen having a helical groove, applying pure torsion to the specimen, measuring the fracture torque, measuring the crack length, and calculating the mixed mode fracture toughness from the fracture torque and the crack length.
The calculation of mixed mode fracture toughness is carried out with a computer program which comprises the steps of: establishing a finite element mesh for a cylindrical specimen under pure torsion to generate an equibiaxial tension/compression stress field on xc2x145xc2x0-pitched orthogonal planes of the finite elements along the right conoids, and a plane strain condition is maintained on every plane normal to the helical groove; establishing 3-D isoparametric finite element meshes with singular elements around the 3-D spiral crack front to simulate rxe2x88x92xc2xd singularity at the crack tip; simulating spiral crack front and crack propagation orientation along the right conoids; prescribing boundary conditions with free axial displacement to simulate pure torsion loading; applying initial end rotation to the finite element model with a given final crack length to determine the corresponding end torque; iterating the end torque step to match the end torque with the measured fracture torque to determine the final end rotation of the finite element model; determining the crack tip opening displacement based on the stress/strain field derived from the calculated final end rotation; verifying that the triaxial stresses and T-stress fields around the crack tip at fracture are positive to ensure a high constraint state is achieved; determining stress intensity factors KI, KII, and KIII from the crack tip opening displacement; and utilizing the stress intensity factors KI, KII, and KIII information and strain energy density criteria to determine the mixed mode fracture toughness.